Balancing energy efficiency and functional demand via bimodal coupling optimization in biological rhythms

Biological rhythms are governed by intricate interactions among oscillatory subsystems, yet how they balance functional demands and energy efficiency remains unclear. We present a bimodal coupling optimization strategy where physiological systems alternate between synchronized (energy-saving) and desynchronized (function-priority) coupling modes. Using the water-filling principle developed in communications engineering, we derive necessary optimality conditions showing that energy-efficiency (oxygen uptake per cardiac work) maximization requires synchronized heart rate(HR)-respiration oscillations.

Then, system modeling confirms task/stress-induced oxygen demands enhance oxygen uptake at the cost of desynchronization and reduced efficiency. Experiments reveal a 70.36% decrease in HR-respiration synchronization during arithmetic versus relaxation, enabling 4.43% higher oxygen uptake but with 11.38% lower energy efficiency. This bimodal coupling optimization strategy is also evident in pancreatic islets, with their insulin/glucagon oscillator alternating between in-phase (energy-saving) and anti-phase (rapid glucose reduction) coupling.

This framework, integrating engineering and life sciences, reveals a universal regulatory principle for biological oscillatory systems. This work was supported by the Innovation Project [grant number ZT-001-002-05]. State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada The authors declare no competing interests.

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Zhang, J., Han, J. & Xie, LL. Balancing energy efficiency and functional demand via bimodal coupling optimization in biological rhythms. Commun Biol (2026). https://doi.org/10.1038/s42003-026-10950-1 DOI: https://doi.org/10.1038/s42003-026-10950-1